We consider the division of a finite number of homogeneous divisible items among three players. Under the assumption that each player assigns a positive value to every item, we characterize the optimal allocations and we develop two exact algorithms for its search. Both the characterization and the algorithm are based on the tight relationship two geometric objects of fair division: the Individual Pieces Set (IPS) and the Radon-Nykodim Set (RNS).
Dividing homogeneous divisible goods among three players / Dall'Aglio, Marco; DI LUCA, Camilla; Milone, Lucia. - In: DAGSTUHL REPORTS. - ISSN 2192-5283. - Volume 6, Issue 6:(2016), pp. 10-25. ((Intervento presentato al convegno Dagstuhl Seminar 16232 on Fair Division. Edited by Yonatan Aumann, Jérôme Lang, and Ariel D. Procaccia. tenutosi a Dagstuhl, Germania nel 5-10 giugno 2016 [10.4230/DagRep.6.6.10].
Dividing homogeneous divisible goods among three players
Marco Dall'Aglio
Membro del Collaboration Group
;Camilla Di LucaMembro del Collaboration Group
;Lucia MiloneMembro del Collaboration Group
2016
Abstract
We consider the division of a finite number of homogeneous divisible items among three players. Under the assumption that each player assigns a positive value to every item, we characterize the optimal allocations and we develop two exact algorithms for its search. Both the characterization and the algorithm are based on the tight relationship two geometric objects of fair division: the Individual Pieces Set (IPS) and the Radon-Nykodim Set (RNS).
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